Data representation Study Guide

Analogue sound, such as speech or music, is naturally continuous and infinitely variable. Computers, however, operate using discrete binary data. To represent analogue sound digitally, a process called sampling is used. This process involves converting the continuous sound wave into a series of discrete numerical values. First, the sound wave's amplitude (its height or intensity) is measured at regular intervals. The frequency of these measurements is called the sample rate, measured in samples per second (Hertz). The time between two consecutive samples is the sample interval. Each measured amplitude is then assigned a numerical value, and the precision of this value is determined by the bit depth. A higher bit depth means more possible amplitude values, leading to a more accurate representation of the original sound. Finally, these numerical values are converted into binary, allowing the computer to store and process the sound.

Binary representation is fundamental to how computers store and process data, using only two states, 0 and 1. However, this system has inherent limitations when the quantity of available bits is constrained. The key limitation is that a finite number of bits can only represent a finite range of values. For integers, this directly translates to a maximum positive and negative value that can be stored. If a calculation results in a number exceeding this maximum, it leads to 'overflow' errors. For fractional numbers, a limited number of bits means that not all real numbers can be represented precisely, resulting in 'rounding' errors or 'truncation'. For example, representing 1/3 in binary with a finite number of bits will always be an approximation. Similarly, images and sounds, which are represented by discrete samples, suffer from 'quantisation' errors when insufficient bits are used for each sample, leading to a loss of detail or fidelity. The greater the number of bits available, the wider the range and the higher the precision of the representation, mitigating these limitations.